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Objective Methods Results Discussion Designing Clinical Trials for Testing Overall Survival in the Presence of Crossover at Progression Fang Xia, Stephen L. George Duke University May, 2014 1 / 14 Objective Methods Results Discussion Objective To present a design tool to assess the power for OS in the presence of treatment switching or crossover after progression from the control treatment to the experimental treatment 2 / 14 Objective Methods Results Discussion Multi-state Model Figure 1 : A simple multi-state model. 3 / 14 Objective Methods Results Discussion Multi-state Model Notation from Fleisher et al (2009) TTP: time to progression X : time to death without progression OS 0 : time until death after progression (also noted as SPP) PFS =⇢min(TTP, X ) TTP + OS 0 OS = PFS if TTP < X otherwise 4 / 14 Objective Methods Results Discussion Multi-state Model with Crossover p: the probability of crossover for control patients C 3 (t): the hazard function for non-crossover control patients C 4 (t): the hazard function for control patients who crossover Figure 2 : Multi-state model for control arm with crossover to experimental treatment after progression. 5 / 14 Objective Methods Results Discussion Relationship between PFS and OS Assumption The time in each state is exponentially distributed TTP, X and OS’ are independent Then PFS = min{TTP, X } ⇠ Exp( 1 + 2 ) Probability of death before progression: ! = 2 1+ 2 The distribution function of OS can be derived by extending the results of Fleisher et al (2009) to the case of crossovers 6 / 14 Objective Methods Results Discussion Design Parameter Required Logrank tests are used to compare the treatments Table 1 : Items to be Specified in the Design ↵1 ↵2 1 1 1 2 Nmax Tmax a MPFS MOS 0 ! p Type I error rate for PFS Type I error rate for OS Power for PFS Power for OS Maximum feasible sample size Maximum study duration Accural rate Median PFS Median OS’ (control-no crossover/crossover; experimental) Probability of death before progression Probability of crossover (control) 7 / 14 Objective Methods Results Discussion Required Number of Events and Duration of Study for PFS E + E 4(Z↵1 /2 + Z 1 )2 E 1 2 , where = = 2 C C (ln ) C 1 + 2 The expected time to achieve DPFS events can be derived as in George and Desu (1974) by solving the following equation for t DPFS = DPFS at ⇤ = [(1 2 exp t C t(exp C Ct ⇤ ⇤ ) ) + (1 exp t E t(exp E Et ⇤ ⇤ ) )] where t ⇤ is the minimum of t and the accural time T. 8 / 14 Objective Methods Results Discussion Required Number of Events and Duration of Study for OS The situation for OS is more complicated because the hazard functions and hazard ratios are not constant Want to determine the required OS events DOS and the optimal sample size N ⇤ N ⇤ : the smallest sample size N that achieves the appropriate statistical power for OS within the maximum allowable expected study duration Tmax Nmin : 1.25 ⇤ DPFS Nmax : the pre-specified maximum sample size allowed 9 / 14 Objective Methods Results Discussion Required Number of Events and Duration of Study for OS Figure 3 : Tree diagram for determining the optimal sample size. 10 / 14 Objective Methods Results Discussion Simulation Example: Hazard Ratios for OS Figure 4 : Hazard Ratios for OS 11 / 14 Objective Methods Results Discussion Discussion We present a design tool to assess the power for testing OS in the presence of treatment switching or crossover after progression from the control treatment to the experimental treatment The approach taken here enables one to assess the power for testing OS under various realistic scenarios and to check the sensitivity of the power to changes in the assumed model parameters in the model Possible to further develop the process to include prognostic factors, loss to follow up, time-varying intensity functions for the multi-state model etc. 12 / 14 Objective Methods Results Discussion References 1. U.S. Food and Drug Administration. Guidance for Industry: Clinical Trial Endpoints for the Approval of Cancer Drugs and Biologics 2007. 2. Korn RL and Crowley JJ. Overview: Progression-Free Survival as an Endpoint in Clinical Trials with Solid Tumors. Clin Cancer Res. 2013; 19: 2607-12. 3. Ghimire S, Kyung E and Kim E. Reporting Trends of Outcome Measures in Phase II and Phase III Trials Conducted in Advanced-Stage Non-small-cell Lung Cancer. Lung. 2013; 191: 313-9. 4. Carroll KJ. Analysis of progression-free survival in oncology trials: some common statistical issues. Pharm Stat. 2007; 6: 99-113. 5. Fleming TR, Rothmann MD and Lu HL. Issues in using progression-free survival when evaluating oncology products. J Clin Oncol. 2009; 27: 2874-80. 6. Panageas KS, Ben-Porat L, Dickler MN, Chapman PB and Schrag D. When you look matters: the effect of assessment schedule on progression-free survival. J Natl Cancer Inst. 2007; 99: 428-32. 7. Hougaard P. Multi-state Models: A Review. Lifetime Data Anal. 1999; 5: 239-64. 8. Fleischer F, Gaschler-Markefski B and Bluhmki E. A statistical model for the dependence between progression-free survival and overall survival. Statistics in Medicine. 2009; 28: 2669-86. 9. Broglio KR and Berry DA. Detecting an Overall Survival Benefit that Is Derived From Progression-Free Survival. J Natl Cancer Inst. 2009; 101: 1642-9. 10. Redman MW, Goldman BH, LeBlanc M, Schott A and Baker LH. Modeling the Relationship between Progression-Free Survival and Overall Survival: The Phase II/III Trial. Clin Cancer Res. 2013; 19: 2646-56. 11. Zhang LJ, Ko CW, Tang SH and Sridhara R. Relationship Between Progression-Free Survival and Overall Survival Benefit: A Simulation Study. Ther Innov Regul Sci. 2013; 47: 95-100. 12. George SL and Desu MM. Planning the size and duration of a clinical trial studying the time to some critical event. J Chronic Dis. 1974; 27: 15-24. 13 / 14 Objective Methods Results Discussion Thank you. 14 / 14